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ICSE Class 10 Physics Question 16 of 27

Solved 2024 Question Paper ICSE Class 10 Physics — Question 5

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5
Question

Question 5(ii)

Light travels a distance of ‘10x’ units in time ‘t1’ in vacuum and it travels a distance of ‘x’ units in time ‘t2’ in a denser medium. Using this information answer the question that follows :

(a) ‘Light covers a distance of ‘20x’ units in time ‘t1’ in diamond.’ State true or false.

(b) Calculate the refractive index of the medium in terms of ‘t1’ and ‘t2’.

Answer

(a) False because speed of light in vacuum is highest and diamond is a denser medium so speed of light will be lower and hence, it can not travel a distance 20x in diamond which is two times of distance travelled by light in vacuum.

(b) Given,

Distance travelled by light in vacuum = 10x

Time taken by light in vacuum = t1

Distance travelled by light in the medium = x

Time taken by light in diamond = t2

As,

Speed of light in vacuum (c)=Distance travelled by light in vacuumTime taken by light in vacuum=10xt1\text {Speed of light in vacuum (c)} = \dfrac {\text {Distance travelled by light in vacuum}}{\text {Time taken by light in vacuum}}= \dfrac {10\text x}{\text t_1}

and

Speed of light in diamond (v)=Distance travelled by light in diamondTime taken by light in diamond=xt2\text {Speed of light in diamond (v)} = \dfrac {\text {Distance travelled by light in diamond}}{\text {Time taken by light in diamond}}= \dfrac {\text x}{\text t_2}

then,

The refractive index of diamond=Speed of light in vacuum (c)speed of light in diamond (v)=10xt1xt2=10t2t1\text {The refractive index of diamond} = \dfrac{\text{Speed of light in vacuum (c)}}{\text {speed of light in diamond (v)}}= \dfrac{\dfrac {10\text x}{\text t_1}}{\dfrac {\text x}{\text t_2}} \\[1em] =\dfrac{10 \text t_2}{\text t_1}